We survey some recent results on local geometric properties of real submanifolds of
complex space. Our main focus is on the structure and properties of mappings between such …

We consider local CR-immersions of a strictly pseudoconvex real hypersurface $
M\subset\bC^{n+ 1} $, near a point $ p\in M $, into the unit sphere $\mathbb S\subset\bC^{n+ …

We show that germs of local real-analytic CR automorphisms of a real-analytic hypersurface
M in C 2 at a point p∈ M are uniquelydetermined by their jets of some finite order at p if and …

Results on finite determination and convergence of formal mappings between smooth
generic submanifolds in ℂ N are established in this article. The finite determination result …

We provide a new way of simultaneously parametrizing arbitrary local CR maps from real-
analytic generic manifolds $ M\subset\mathbb {C}^ N $ into spheres $\mathbb {S}^{2N' …

An approach is suggested to equivalence and embedding problems for smooth CR-
submanifolds of complex spaces (and, more generally, for abstract CR-manifolds) in terms of …

We study the regularity and algebraicity for mappings into classical domains. Among other
things, we establish everywhere regularity and algebraicity results for C^ 2 C 2 CR maps …

We construct a family of small analytic discs attached to Levi non-degenerate hypersurfaces
in C^ n+ 1 C n+ 1, which is globally biholomorphically invariant. We then apply this …

We prove a smooth version of the classical Schwarz reflection principle for CR mappings
between an abstract CR manifold $ M $ and a generic CR manifold embedded in euclidean …

Let M, M'be smooth real hypersurfaces in N-dimensional space and assume that M is k-
nondegenerate at a point p in M. We prove that holomorphic mappings that extend smoothly …